The test setup was:
Campaign A, weight 99, single text banner, banner weight irrelevant
Campaign B, weight 1, single text banner, banner weight irrelevant
Text Zone 1, linked to both campaigns, chained to Zone B
Text Zone 2, empty
Test page with two async tags with the "do not show the same banner" flag.
Zone 1 was pretty much always showing A, while Zone 2 was showing B. To be fair you don't even need chained zones: just repeat the tag for zone 1, unless you need to keep track of the "positions".